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A  SCALE  FOR  MEASURING  THE  QUALITY  OF 
HANDWRITING  OF  SCHOOL  CHILDREN 

During  the  past  few  months  the  Division  of  Education  of 
the  Russell  Sage  Foundation  has  been  conducting  a  study  of 
handwriting  with  the  purpose  of  producing  a  scale  for  measuring 
the  quality  of  the  handwriting  of  school  children  of  the  upper 
elementary  grades.  This  report  describes  the  investigation  and 
presents  the  scale  which  it  has  produced. 

The  investigation  consisted  of  a  study  of  the  legibility  of 
1578  samples  of  the  handwriting  of  children  of  the  upper  ele- 
mentary grades  of  forty  school  systems  in  thirty-eight  states. 
The  degree  of  legibility  of  the  samples  was  ascertained  by  a 
series  of  15,780  accurately  timed  readings  made  by  ten  paid 
investigators. 

The  quality  of  each  sample  of  writing  was  determined  by  its 
degree  of  legibility  as  shown  by  these  readings,  the  assumption 
being  that  that  writing  is  best  for  practical  purposes  which  can 
be  most  easily  read. 

The  scale  itself  is  a  sheet  of  paper  measuring  9  by  36  inches 
and  having  eight  divisions  from  end  to  end.  In  each  division 
are  samples  of  handwriting.  As  one  proceeds  along  the  strip 
from  left  to  right  these  samples  are  progressively  better.  They 
have  been  so  chosen  that  each  one  is  as  much  better  than  the 
one  before  as  that  is  better  than  the  preceding.  That  is  to  say, 
all  of  the  steps  are  equal  (to  within  one-tenth  of  one  step). 
These  samples  or  steps  have  been  assigned  the  values  20,  30, 
40,  50,  60,  70,  80,  and  90.  These  values  have  been  chosen 
rather  than  any  others  because  teachers  are  familiar  with  them 
as  marks  used  in  scoring  children's  school  work. 

In  order  to  measure  the  value  of  any  given  sample  of  writing 
all  that  is  necessary  is  to  slide  it  along  the  scale  until  a  writing 
of  the  same  quality  is  found.  By  looking  at  the  top  of  the  scale 
the  number  corresponding  to  the  quality  of  the  writing  will  be 
found  and  this  number  represents  the  value  of  the  writing  being 
measured. 

3 

272010 


In  order  to  facilitate  this  measuring  there  have  been  placed 
at  each  point  samples  of  vertical,  medium  slant  and  extreme 
slant  writing,  all  of  equal  value.  Thus,  the  sample  being  measured 
may  be  compared  with  samples  on  the  scale  written  in  the 
corresponding  style  of  slant.  The  three  slants  used  on  the  scale 
include  over  95  per  cent  of  the  ordinary  writings  of  school 
children. 

In  order  to  facilitate  comparison  with  the  ordinary  writings 
of  school  children  the  scale  has  been  printed  in  blue  ink,  which, 
as  nearly  as  possible,  matches  the  color  of  the  ink  most  commonly 
used  in  the  public  schools.  For  the  same  reason,  the  scale  has 
been  printed  on  paper  corresponding  in  color  with  the  paper 
ordinarily  used  in  schools. 

In  conducting  the  investigation  several  important  facts 
have  been  brought  to  light.  The  most  significant  of  these  is 
that  the  factors  of  most  importance  in  determining  legibility  of 
handwriting  are,  first,  the  spacing  between  the  words,  and 
second,  the  spacing  between  the  lines.  Many  handwritings 
which  look  well  but  are  so  spaced  that  the  words  run  into  each 
other  are  very  difficult  to  read,  and,  on  the  other  hand,  writings 
well  spaced  but  having  somewhat  irregular  letters  are  frequently 
quite  readily  legible. 

With  respect  to  the  styles  of  writing  the  investigation  shows 
that  vertical  writings  are  in  general  the  most  legible,  medium 
slants  next,  and  extreme  slants  least  legible. 

The  present  scale  is  not  presented  as  offering  a  standard,  but 
as  furnishing  a  means  for  measuring  so  that  teachers,  principals 
and  supervisors  may  measure  the  results  of  the  pupils'  work, 
discover  which  methods  produce  the  best  results,  and  on  the 
basis  of  such  study  and  experiment  erect  their  own  standards  to 
which  pupils  may  be  expected  to  attain. 

The  Thorndike  Scale 
This  is  not  a  pioneer  piece  of  work  in  this  field,  although  it 
is  different  in  method  from  anything  of  the  sort  previously 
attempted.  The  credit  of  developing  the  first  measuring  scale 
for  handwriting  belongs  to  Professor  Edward  L.  Thorndike  of 
Teachers  College,  Columbia  University.  The  publication,  in 
March,  1910,  of  his  handwriting  scale  constituted  a  most  impor- 
tant contribution  not  only  to  experimental  pedagogy  but  to  the 
entire  movement  for  the  scientific  study  of  education. 


As  Professor  Thorndike  says  in  his  introduction,  previous 
to  that  time  educators  were  in  the  same  condition  with  respect 
to  handwriting  as  were  students  of  temperature  before  the  dis- 
covery of  the  thermometer.  Just  as  it  was  then  impossible  to 
measure  temperature  beyond  the  very  hot,  hot,  warm,  cool,  etc., 
of  subjective  opinion,  so  it  had  been  impossible  to  estimate  the 
quality  of  handwriting  except  by  such  vague  standards  as  one's 
personal  opinion  that  given  samples  were  very  bad,  bad,  good, 
very  good,  etc.  Professor  Thorndike's  scale  for  the  handwriting 
of  children  is  based  on  the  average  or  median  judgments  of  some 
23  to  55  judges  who  graded  samples  of  writing  into  groups  by 
what  they  considered  equal  progressive  steps  in  general  merit. 

Legibility  as  a  Criterion 

The  method  by  which  the  present  scale  has  been  produced, 
and  the  criterion  on  which  it  rests  as  a  basis,  differ  radically  from 
those  adopted  by  Professor  Thorndike.  The  difference  in  the 
bases  is  that  in  the  present  case  legibility  has  been  adopted  as  a 
criterion  for  rating  the  different  samples  in  place  of  "general 
merit"  used  as  the  basis  of  Thorndike's  scale.  This  change 
substitutes  function  for  appearance  as  a  criterion  for  judging 
handwriting. 

There  are  two  arguments  for  adopting  the  new  criterion. 
In  the  first  place  the  prime  purpose  of  writing  is  to  be  read,  and 
hence  it  has  seemed  worth  while  to  adopt  "readability"  as  the 
basis  for  rating  samples  of  handwriting.  In  the  second  place 
legibility  possesses  the  advantage  of  being  measurable  in  definite 
quantitative  units  through  finding  the  amount  of  time  required 
to  read  with  a  given  degree  of  accuracy  a  given  amount  of  matter 
written  in  the  handwriting  being  studied.  The  criterion  of 
general  merit  is  not  susceptible  of  any  such  exact  evaluation. 

The  method  whereby  the  new  scale  has  been  produced 
differs  from  the  method  employed  in  producing  the  previous  scale 
in  that  it  is  based  on  the  distribution  of  the  recorded  times  re- 
quired on  the  average  by  a  number  of  readers  to  read  the  samples 
of  writing,  rather  than  on  the  average  of  their  judgments  con- 
cerning what  they  considered  equal  steps  in  general  merit. 

Preliminary  experimenting,  begun  in  November,  191 1,  showed 
that  the  most  satisfactory  way  to  discover  the  relative  legibility 
of  different  samples  of  handwriting  is  through  finding  the  rate  in 
words  per  minute  at  which  it  is  possible  to  read  each  sort  of 


writing.  In  order  to  secure  a  large  number  of  samples  of  the 
writing  of  school  children  of  the  upper  elementary  grades  of  such 
a  character  that  they  could  be  justly  rated  by  means  of  this 
method,  it  was  necessary  to  observe  rigidly  a  number  of  exacting 
conditions.  The  first  step  was  to  secure  the  co-operation  of 
superintendents  of  schools  in  a  number  of  different  cities  in 
different  parts  of  the  country  so  that  the  samples  of  writing  should 
so  far  as  possible  represent  a  random  selection  and  not  be  typical 
merely  of  the  writings  of  pupils  of  a  given  city  or  section.  This 
was  done  through  correspondence  which  resulted  in  securing 
the  co-operation  of  the  superintendents  of  schools  in  the  following 
cities : 

Aberdeen,  South  Dakota  Manchester,  New  Hampshire 

Albuquerque,  New  Mexico  Milwaukee,  Wisconsin 

Ardmore,  Oklahoma  Mobile,  Alabama 

Atlanta,  Georgia  Nashville,  Tennessee 

Baltimore,  Maryland  Newark,  New  Jersey 

Bloomington,  Indiana  New  Orleans,  Louisiana 

Charleston,  South  Carolina  Newton,  Massachusetts 

Cheyenne,  Wyoming  New  York  City,  New  York 

Cleveland,  Ohio  Omaha,  Nebraska 

Connersville,  Indiana  Peoria,  Illinois 

Danbury,  Connecticut  Providence,  Rhode  Island 

Denver,  Colorado  Raleigh,  North  Carolina 

Des  Moines,  Iowa  Reno,  Nevada 

Elmira,  New  York  Roanoke,  Virginia 

Harrisburg,  Pennsylvania  St.  Paul,  Minnesota 

Houston,  Texas  Salt  Lake  City,  Utah 

Jackson,  Mississippi  Springfield,  Massachusetts 

Kalamazoo,  Michigan  Washington,  D.  C. 

Lewiston,  Maine  Wheeling,  West  Virginia 

Louisville,  Kentucky  Wilmington,  Delaware 

Conditions  Under  Which  the  Samples  Were  Secured 
The  next  requisite  was  that  all  of  the  samples  of  handwriting 
should  be  produced  under  conditions  as  uniform  as  possible. 
This  end  was  attained  by  having  all  the  writing  done  on  sheets  of 
unruled  paper  of  uniform  size  and  quality  furnished  to  the  differ- 
ent school  systems  from  the  office  of  the  Foundation.  At  the 
top  of  each  sheet  of  paper  were  15  lines  of  typewritten  material 
from  which  the  pupils  in  every  case  copied  as  much  as  they  could 
at  their  ordinary  rate  of  writing  in  just  ten  minutes.  These 
15  lines  of  typewriting  were  not  composed  of  ordinary  prose. 


They  were  made  up  of  material  selected  from  Washington  Irving's 
"Rip  Van  Winkle"  and  "The  Legend  of  Sleepy  Hollow,"  and 
in  each  case  the  first  20  words  were  in  the  original  order  while  the 
rest  of  the  15  lines  of  the  material  was  composed  of  words  thrown 
out  of  context  in  such  a  way  as  to  convey  no  meaning.  The  ob- 
ject of  having  the  first  20  words  in  their  original  order  was  to 
secure  sensible  samples  for  the  final  scale.  It  was  afterwards 
found  that  this  feature  was  of  doubtful  value.  The  object  of 
having  the  rest  of  the  material  thrown  out  of  context  was  to 
secure  samples  such  that  the  readers  would  be  in  no  way  aided 
by  the  context  but  would  have  to  decipher  each  word  separately. 

A  further  object  was  to  secure  material  which  the  readers 
could  not  memorize.  To  insure  this  even  more  fully  the  material 
was  put  together  in  the  different  copies  in  varied  combinations 
so  that  there  were  used  in  all  some  30  different  sets  of  copy,  all 
of  which  were  made  up  from  the  same  general  material.  As  a 
further  precaution  very  unusual  words  and  difficult  names  were 
omitted  from  the  copy. 

Uniform  sheets  of  instructions  were  supplied  to  the  superin- 
tendents and  teachers  co-operating  in  the  investigation  and 
care  was  taken  to  avoid  securing  samples  from  either  the  best  or 
worst  classes  in  any  city.  The  teachers  were  also  warned  against 
suggesting  to  the  children  that  they  attempt  to  write  either 
unusually  well  or  unusually  rapidly.  The  co-operation  of  both 
superintendents  and  teachers  was  gratifyingly  prompt,  and  in 
general  it  was  evident  that  the  instructions  were  faithfully 
followed. 

Conditions  Under  Which  the  Samples  Were  Read  and 
Scored 
As  a  result  of  these  preliminaries  1578  satisfactory  samples 
of  children's  handwriting  were  selected  from  those  secured. 
When  they  were  received  at  the  New  York  office  each  sample 
was  given  a  serial  number  and  on  each  sheet  was  placed  the  im- 
print of  a  stamp  having  spaces  designed  to  receive  all  of  the 
different  data  concerning  that  particular  sample.  The  next 
step  was  to  sort  the  specimens  into  groups  of  25  in  such  a  way 
that  there  were  no  duplicates.  These  packages  were  then 
turned  over  to  a  group  of  ten  readers  who  in  turn  read  each 
sample,  recorded  by  means  of  a  stop-watch  the  exact  time  re- 
quired to  complete  the  reading,  and  entered  the  result  in  the 


8 

appropriate  space.  This  reading  in  each  case  included  only  the 
material  which  had  been  thrown  out  of  context;  that  is  to  say, 
the  first  20  words  were  omitted  in  the  readings. 

No  volunteer  assistance  was  utilized  in  any  of  the  processes, 
all  of  the  readers  being  employed  and  the  work  done  under  close 
supervision.  The  same  ten  readers  were  employed  during  the 
entire  investigation.  This  force  consisted  of  four  men  and  six 
women  and  included  the  author  of  the  present  report,  his  secre- 
tary, three  university  students,  a  statistician,  a  stenographer, 
a  clerk,  a  former  teacher  and  a  writer  on  sociological  subjects. 

After  each  sample  of  writing  had  been  read  by  the  entire 
ten  people  and  a  record  made  of  the  exact  time  required  by  each, 
the  sum  of  these  times  was  found  and  the  average  time  computed. 
This  average  time  was  recorded  in  seconds  and  another  computa- 
tion was  required  to  express  the  seconds  in  a  decimal  fraction  of 
a  minute.  For  example,  if  the  average  reading  time  for  a  given 
sample  was  77  seconds  this  was  converted  into  1.283  minutes. 

A  careful  count  was  then  made  of  the  exact  number  of  words 
contained  in  the  sample  and  this  number  was  divided  by  the 
decimal  expression  of  the  average  time  required  to  read  it.  The 
result  gave  the  rate  in  v/ords  per  minute  at  which  the  reading  had 
been  done.  For  exam.ple,  in  the  case  just  cited  where  the  average 
of  the  reading  times  was  1.283  minutes,  if  the  number  of  words 
in  the  sample  were,  say,  193  the  resulting  rate  secured  by  dividing 
193  by  1.283  would  be  150.4  words  per  minute. 

The  student  famihar  with  the  mathematics  of  speeds  and 
rates  will  note  that  this  process  does  not  give  the  same  result 
as  that  which  would  have  been  secured  by  getting  the  average  of 
the  rates  at  which  each  person  read  instead  of  the  average  of  the 
times  of  the  several  readings.  The  method  used  was  adopted  as 
giving  a  truer  reflection  of  the  relative  degrees  of  legibility  of 
the  different  samples  of  writing. 

As  each  reader  read  each  sample  a  record  was  kept  not  only 
of  the  time  required  but  of  the  number  of  words  not  deciphered. 
In  the  final  computations  samples  were  thrown  out  in  which  the 
number  of  such  omissions  exceeded  on  the  average  one  per 
minute. 

The  process  described  was  gone  through  with  for  each  one  of 
the  1578  samples  of  writing.  This  work  entailed  a  total  of 
15,780  timed  readings,  1578  additions  each  made  twice,  the 
counting  of  some  181,304  words  twice,  and  3156  divisions  to  the 


third  decimal  place.  The  principal  result  was  a  figure  on  each 
sample  giving  the  rate  in  words  per  minute  at  which  it  had  been 
read  by  the  ten  readers. 

At  the  conclusion  of  the  work  of  making  the  readings  a  study 
was  made  to  discover  to  what  extent  the  readers  had  increased 
their  average  speed  through  practice.  This  brought  to  light  the 
fact  that  there  had  been  a  distinct  though  small  increase  after 
the  initial  stages.  Accordingly  the  first  75  papers  were  re-read 
by  the  ten  readers  and  the  new  times  substituted  for  the  old  ones. 

Classification  by  Style 

The  next  step  consisted  of  classifying  the  samples  according 
to  the  style  of  the  letters.  The  first  attempt  was  to  rate  accord- 
ing to  the  heaviness  or  thickness  of  the  lines  used  in  forming  the 
letters.  This  was  found  to  be  impracticable.  Among  each 
hundred  samples  the  readers  chose  only  about  three  as  being 
written  in  notably  light  lines  and  only  about  four  as  being 
written  with  exceptionally  heavy  strokes. 

Another  attempt  was  made  to  classify  the  samples  as  being 
written  with  large,  flowing  letters,  medium  ones,  and  small, 
compact  letters.  This  again  was  found  to  be  impracticable. 
Considerable  variations  in  the  size  of  the  letters  were  common, 
but  less  than  10  per  cent  of  the  whole  number  of  samples  could 
fairly  be  classified  as  being  written  in  letters  either  notably  small 
and  compact  or  large  and  flowing.  A  similar  result  was  found 
when  the  attempt  was  made  to  classify  the  writings  according 
as  the  letters  were  characteristically  angular  or  circular. 

The  final  solution  of  the  matter  came  through  basing  the 
classifications  of  style  on  the  slant  of  letters.  Five  classes  were 
defined  on  the  basis  of  the  judgments  of  a  number  of  competent 
judges  who  were  asked  to  classify  several  hundred  samples  into 
groups  according  as  in  their  opinions  the  writings  were  "vertical," 
"medium  slant,"  "extreme  slant,"  "back  hand"  and  "mixed." 

On  the  basis  of  these  groupings  "vertical  writing"  was 
defined  as  writing  in  which  the  characteristic  slant  of  the  letters 
lay  between  90°  and  80°  from  the  horizontal.  The  limits  of 
"medium  slant"  were  defined  in  a  similar  way  as  lying  between 
80°  and  55°,  and  those  of  "extreme  slant"  as  ranging  from  55° 
to  30°.  "  Back  hand  "  was  defined  as  being  any  writing  in  which 
the  characteristic  slant  of  the  letters  was  to  the  left  of  vertical, 
and  "mixed"  was  a  writing  composed  of  a  combination  of  two 


10 

or  more  styles.  For  purposes  of  convenient  classification  ver- 
tical writing  was  designated  as  "A",  medium  slant  as  "B", 
extreme  slant  as  "C",  back  hand  as  "D"  and  mixed  as  "E". 

On  the  basis  of  this  classification  protractors  were  constructed 
of  transparent  celluloid  and  with  their  aid  each  one  of  the  1578 
samples  was  rated  on  the  basis  of  the  slant  of  the  letters  and 
the  sample  marked  with  the  appropriate  symbol  to  indicate  to 
which  of  the  five  classes  it  belonged.  The  results  of  this  classi- 
fication were  as  follows: 

Slant                                                           Number  Per  Cent 

Class  A  (vertical) 255  16.2 

Class  B  (medium  slant) 670  42.5 

Class  C  (extreme  slant) 580  36.7 

Class  D  (back  hand) 27  1.7 

Class  E  (mixed  slants) 46  2.9 


1578  lOO.O 


Vl 


Locating  Equal  Steps  on  the  Scale 
When  tiie  entire  1578  samples  had  been  scored  and  each 
marked  with  the  rate  at  which  it  had  been  read  by  the  ten  readers, 
they  were  arranged  in  order  in  one  long  series  beginning  with  the 
sample  having  the  lowest  rating  and  proceeding  on  through  the 
entire  group  to  the  final  sample  having  the  highest  rating  of  all. 
This  arrangement  showed  that  there  were  only  a  few  very  bad 
samples  that  had  been  read  very  slowly,  many  samples  of  medium 
grade  that  had  been  read  at  medium  rates  and  only  a  few  of 
the  highest  grade  that  were  so  clear  and  regular  that  they  had 
been  read  at  the  most  rapid  rates. 

The  next  step  was  to  study  the  distribution  further  to  dis- 
cover its  characteristics.  By  counting  half  way.  through  the 
distribution  the  point  was  found  at  which  exactly  half  the  cases 
lay  below  and  the  other  half  above.  The  sample  at  this  point 
was  rated  175.7,  indicating  that  it  was  read  at  the  rate  of  175.7 
words  per  minute.  As  it  was  exactly  at  the  central  point,  one 
half  of  the  samples  were  read  more  slowly  and  the  other  half 
more  rapidly.  In  the  same  way  the  samples  one-quarter  and 
three-quarters  of  the  way  through  the  distribution  were  located 
and  found  to  be  rated  at  162.8  and  186.9  respectively.  This 
gave  the  following : 

Point  in  Distribution  Rating  of  Sample 

One  quarter 162.8 

One  half 175-7 

Three  quarters 186.9 


II 

The  immediately  noticeable  feature  of  these  figures  is  that 
the  difference  between  the  rating  of  the  sample  at  the  one-quarter 
point  and  that  at  the  one-half  point  is  greater  than  the  difference 
between  the  rating  of  this  second  sample  and  that  of  the  one  at 
the  three-quarters  point.  In  the  first  case  it  is  12.9,  while  in 
the  second  it  is  only  11. 2.  This  taken  together  with  the  fact 
that  in  the  distribution  as  a  whole  we  found  few  samples  with 
very  low  ratings,  many  with  medium  ones,  and  few  with  very 
high  ones  suggested  the  possibility  that  we  were  here  dealing 
with  what  is  termed  a  "normal  distribution"  and  that  equal 
steps  on  the  scale  on  which  it  was  based  were  expressed  in  pro- 
gressively smaller  numbers  of  words  read  per  minute. 

Normal  distributions  are  familiar  to  students  of  social, 
anthropological  and  biological  problems.  The  characteristics  of 
such  a  distribution  may  be  illustrated  by  supposing  that  we 
gather  data  as  to  the  heights  of  a  great  many  adult  men  of  a  given 
nationality.  Now  suppose  we  arrange  these  heights  in  the  order 
of  their  magnitude.  What  we  shall  always  find  is  that  at  about 
the  middle  point  between  the  extremes  will  be  found  a  large 
number  of  approximately  equal  heights  crowded  together. 
This  expresses  the  truism  that  most  men  are  of  "about  average 
height."  A  little  on  each  side  of  the  middle  point  will  be  found 
a  good  many  measures  although  not  so  many  as  nearer  the  central 
point.  This  expresses  the  fact  that  there  are  a  good  many  men 
of  something  less  than  average  height  and  a  considerable  number 
somewhat  above  the  average  height.  As  we  get  further  away 
from  the  central  point  this  process  continues  in  a  diminishing 
scale  of  proportion  until  as  we  get  near  the  extreme  ends  of  the 
scale  the  numbers  thin  off  rapidly  and  become  exceedingly  small. 
This  expresses  the  fact  that  there  are  very  few  dwarfs  and  very 
few  giants.  Many  similar  examples  might  be  cited  of  normal 
distributions  in  other  fields.  The  laws  which  govern  such 
distributions  have  been  most  accurately  determined  through 
searching  investigations  extending  over  many  years. 

Assuming  that  the  distribution  of  the  ratings  of  our  1578 
samples  of  handwriting  was  a  normal  distribution  plotted  on  a 
base,  line  running  from  o  to  100,  the  locations  of  the  points  10, 
20,  30,  and  so  on  were  determined  and  the  corresponding  samples 
found.  This  is  illustrated  in  graphic  form  in  the  accompanying 
diagram  which  represents  a  normal  distribution  of  1578  cases 
plotted  on  a  base  line  on  which  o  is  the  location  of  the  sample 


12 


having  the  lowest  rating  and  lOO  that  of  the  one  having  the 
highest  rating. 


Curve  of  normal  distribution  plotted  on  base  line  from  o  to  lOO  with  median 
at  50. 


The  average  falls  at  the  point  marked  50  on  the  base  line; 
that  is  to  say,  it  is  half  way  between  the  lower  extreme  and  the 
higher.  The  curve  cutting  the  axis  erected  at  this  point  for  a 
time  remains  almost  parallel  to  the  base  line  on  both  sides  of 
the  axis.  This  expresses  the  fact  that  near  the  average  there 
are  a  large  number  of  values  approximately  equal.  After  a 
time  it  begins  to  slope  away  rapidly  toward  the  base  line.  This 
expresses  the  fact  that  the  cases  soon  begin  to  grow  less  common 
as  we  get  away  from  the  average  on  either  side.  The  curve  is 
symmetrical  on  both  sides,  expressing  the  fact  that  there  are 
equal  deviations  away  from  the  average  both  above  and  below. 
At  each  one  of  the  points  along  the  scale  an  upright  has  been 
erected,  dividing  the  distribution  into  ten  parts.  The  number 
of  cases  falling  within  each  of  the  divisions  thus  made  may  be 
computed  in  the  normal  distribution  and  used  as  the  basis  for 
locating  the  corresponding  points  in  our  distribution  of  ratings. 
This  gave  the  following  results: —    • 


13 

Rating  ik  Words  per 
Point  on  Minute  of  Sample 

Scale  Found  at  each  Point 

90 209.6 

80 202.9 

70 195-8 

60 186.1 

50 1757 

40 163.5 

30 1494 

20 131-2 

The  characteristic  of  this  series  is  that  it  proceeds,  not  by 
even  steps,  but  by  steps  that  are  progressively  larger  as  we  move 
from  the  upper  end  of  the  scale  to  the  lower  one.  This  means 
that  the  successive  downward  steps  on  the  scale  represent  pro- 
gressively greater  departures  from  the  most  readily  legible  sort 
of  writing. 

A  study  of  the  figures  shows  that  the  ratio  of  each  descending 
step  to  the  preceding  is  approximately  117.2  per  cent.  This 
gave  a  series  according  to  theory  and  one  according  to  actual 
count  as  follows: — 

Series  of  Samples  Series  of  Samples 

Point  on                                                             According  to  According  to 

Scale                                                              Actual  Count  Theory 

90 209.6  209.2 

80 202.9  202.7 

70 195-8  I95-I 

60 186.1  186.2 

50 175-7  175-7 

40 163.5  163-4 

30 149-4  149-I 

20 131-2  132-2 

The  agreement  between  the  two  series  is  so  close  as  to  warrant 
substituting  the  theoretic  series  for  the  one  produced  by  actual 
count. 

The  practical  application  of  all  this  in  the  present  instance 
is  that  equal  ascending  steps  in  legibility  are  reflected  by  pro- 
gressively smaller  increments  in  the  rate  at  which  the  writings 
can  be  read.  Conversely,  equal  descending  steps  in  legibility 
are  reflected  by  progressively  greater  decreases  in  the  rate  of 
reading.  A  little  reflection  will  show  how  reasonable  and  in 
accord  with  daily  experience  this  is.  An  almost  illegible  writing 
can  be  deciphered  only  extremely  slowly.  An  only  slightly 
better  one  can  be  read  perhaps  twice  as  fast.  A  still  better 
specimen  can  be  read  somewhat  more  rapidly,  but  this  time  the 
rate  cannot  by  any  possibility  be  doubled.     Thus,  as  we  proceed 


14 

to  increasingly  better  writings,  our  reading  rate  increases  by 
smaller  and  smaller  increments,  until  finally  we  reach  writings 
so  excellent  that  no  increase  in  the  rate  of  reading  short  specimens 
can  be  detected. 

In  the  present  case,  the  steps  on  the  scale  indicate  relative 
positions  in  the  distribution  of  a  relatively  random  selection  of 
writings  of  school  children  of  the  upper  elementary  grades. 
Quality  50  is  such  a  quality  that  one-half  of  the  writings  are 
worse  than  that  quality,  and  the  other  half  better.  Qualities 
60  and  40  are  respectively  equal  distances  above  and  below  the 
50  point.  The  proportion  of  the  total  number  of  samples  lying 
between  qualities  40  and  50  is  equal  to  the  proportion  lying 
between  50  and  60.  Similar  conditions  fix  the  positions  of  each 
pair  of  steps  as  we  proceed  up  and  down  the  scale  away  from  the 
central  point. 

With  respect  to  the  zero  point  on  this  scale,  it  may  appear 
that  the  zero  point  on  a  scale  for  the  legibility  of  writing  ought 
to  represent  a  writing  entirely  unreadable.  The  reason  why  it 
is  not  so  in  this  case  is  that  this  is  a  scale  for  the  measurement  of 
the  writings  of  school  children  of  the  upper  grades,  and  in  the 
nature  of  the  case  the  worst  school  writings  in  upper  grades  can 
never  be  entirely  illegible.  Hence,  an  entirely  unreadable  writ- 
ing is  not  the  zero  point  for  a  scale  of  this  sort.  In  the  same  way, 
the  writing  at  point  100  would  be  the  most  legible  writing  found 
among  the  writings  of  school  children  and  not  an  ideally  perfect 
one.  ^/ 

^  General  Appearance  and  Legibility 
The  investigation  developed  several  important  facts  as  to 
the  relation  between  legibility  and  the  general  appearance  of 
handwritings.  The  most  important  of  these  is  that,  whereas 
extremely  legible  writings  are  almost  invariably  of  good  appear- 
ance, many  writings  of  good  appearance  are  of  relatively  low 
degrees  of  legibility. 

Analysis  of  good-looking  writings  of  low  degrees  of  legibility 
shows  that  their  most  common  shortcoming  is  the  crowding 
together  of  the  words  on  the  line.  This  indicates  that  those 
systems  of  penmanship  are  vicious  that  teach  children  to  space 
their  words  so  closely  that  the  final  stroke  of  the  last  letter  of 
one  word  extends  over  the  initial  stroke  of  the  first  letter  of 
the   following  word.     Next   to   too   close   spacing   horizontally 


15 

comes  too  close  spacing  between  the  lines  as  a  characteristic 
making  for  illegibility. 

Another  common  fault  of  good-looking  writings  that  are  dif- 
ficult to  read  is  the  breaking  of  lines  in  the  middle  of  words  in 
such  a  way  as  to  make  one  word  look  at  first  glance  like  two  words. 
The  absence  of  dots  over  the  i's  and  crosses  on  the  t's  is  also  a 
common  and  important  shortcoming  of  good-looking  writings 
that  are  difficult  to  read. 

The  practical  application  of  all  this  is  that  we  shall  obtain 
the  best  results  in  teaching  writing  by  striving  to  conform  to 
types  that  are  most  readily  legible.  By  so  doing,  we  shall  obtain 
writings  that  are  at  once  the  most  useful  and  the  best  looking. 

Slant  and  Quality 
A  preliminary  study  of  the  relation  between  the  several 
slants  and  the  quality  of  the  writings  indicates  that  in  general 
the  vertical  writings  are  the  most  legible,  the  medium  slants 
next  and  the  extreme  slants  next.  The  number  of  samples  of 
back  hand  and  mixed  slants  is  so  limited  as  to  render  the  data 
with  respect  to  the  speed  of  reading  these  two  styles  of  doubtful 
value.  The  following  figures  show  median  rates  in  words  per 
minute  at  which  the  writings  of  each  style  were  read : — 

Median  Rate  of 
Number  of  Reading  in 

Samples      Words  Per  Mimrre 

Vertical  ("A")  255  180 

Medium  Slant  ("  B  ") 670  176 

Extreme  Slant  ("C") 580  172 

Back  Hand  ("D") 27  168 

Mixed  ("E") 46  I74 

Slant,  Speed,  and  Quality 

The  conditions  under  which  the  samples  were  obtained  pre- 
clude any  extensive  study  as  to  speeds  for  the  reason  that  the 
writing  was  done  from  copy  in  which  the  words  were  thrown 
out  of  context.  This  made  the  copying  of  the  material  a  most 
unusual  exercise  for  the  children,  and  renders  dangerous  any 
conclusions  from  these  data  as  to  the  comparative  writing  rates 
of  children  of  different  grades  and  cities.  Nevertheless,  compari- 
sons between  speeds,  slants  and  qualities  may  be  tentatively 
made,  since  the  writing  conditions  were  equal  for  all  the  children. 

This  comparison  shows  that  there  is  a  slight  but  steady  falling 
off  in  the  average  number  of  words  written  per  minute  as  we  pass 


i6 

from  the  poorer  writings  to  the  better  ones.     The  following 
figures  give  the  comparison: — 

Total         Average  Number 
Number  Number       of  Words  Written 

OF  Samples  of  Words       in  Ten  Minutes 

First  quarter  of  distribution  (poorest 

writings) 394  46,535  nS.i 

Second  quarter  of  distribution 395  46,592  1 1 7-9 

Third  quarter  of  distribution 395  45.449  HS-I 

Fourth  quarter  of  distribution  (best 

writings) 394  42,728  108.4 

Total 1578  181,304  1 14.9 

The  figures  with  respect  to  slants  and  speeds  are  as  follows : — 

Total        Average  Number 
Number  Number    of  Words  Written 

OF  Samples  of  Words      in  Ten  Minutes 

Vertical  ("A") 255  29,402  115. 3 

Medium  Slant  ("B") 670  76,779  114.6 

Extreme  Slant  ("C") 580  67,369  116.1 

Back  Hand  ("D") 27  2,726  loi.o 

Mixed  ("  E ") 46  5,028  109.3 

Total 1578  181,304  1 14.9 

The  foregoing  figures  make  an  even  showing  for  the  different 
styles  which  comes  as  a  distinct  surprise  to  the  writer  of  the 
present  report.  The  comparison  of  qualities  showed  that  the 
vertical  writings  are  the  most  legible  of  the  different  styles.  The 
figures  just  cited  show  that  the  extreme  slant  writings  are  a  little 
ahead  of  the  other  styles  with  respect  to  speed  of  writing.  In 
short,  the  meaning  of  the  figures  is  that  the  different  writings 
are  surprisingly  equal  as  to  legibility  and  the  speed  at  which 
they  are  written. 

Final  conclusions,  however,  as  to  this  and  other  problems 
of  import  in  the  applied  pedagogy  of  handwriting  should  not  be 
reached  until  many  careful  studies  of  children's  writing  have 
been  made.  Such  investigations  should  include  inquiries  to 
determine  the  best  types  of  writing  and  the  most  successful 
methods  of  teaching.  The  present  scale  has  been  produced 
with  the  express  object  of  furnishing  an  instrument  to  facilitate 
the  conduct  of  such  studies  and  to  evaluate  the  results. 


Some  Publications  on  Measurements  in  Education* 

Issued  by  the  Division  of  Education 

Russell  Sage  Foundation 


No.  6i.  The    Relation    of    Physical    Defects    to   School 
Progress.     Leonard  P.  Ayres,  Ph.D. 
A  statistical  study  based  on  7608  cases.     9  pp. 

No.  107.  The  Binet-Simon  Measuring  Scale  for  Intelli- 
gence:   Some  Criticisms  and  Suggestions. 
Leonard  P.  Ayres,  Ph.D. 
A  critical  study  of  these  tests  as  used  in  American 
schools,  and  suggestions  as  to  their  adaptation  to 
our  conditions. 

No.  108.  The  Identification  of  the  Misfit  Child. 
Leonard  P.  Ayres,  Ph.D. 
Data  from  a  study  of  the  age  and  progress  records 
of  school  children  in  twenty-nine  cities. 

No.  no.  The  Relative  Responsibility  of  School  and  So- 
ciety FOR  THE  Over-age  Child. 
Leonard  P.  Ayres,  Ph.D. 
Data  from  a  study  of  the  age  and  progress  records 
of  school  children  in  twenty-nine  cities,  showing  the 
number  of  children  over-age  because  of  late  entrance, 
slow  progress,  and  both  causes  combined. 

No.  112.  The  Relation  Between  Entering  Age  and  Sub- 
sequent Progress  Among  School  Children. 
Leonard  P.  Ayres,  Ph.D. 
Evidence  from  three  investigations  bearing  on  the 
problem  "What  is  the  best  age  to  send  a  child  to 
school?" 

No.  1x6.  The  Measurement  of  Educational  Process  and 
Products. 

Leonard  P.  Ayres,  Ph.D. 
An  account  of  the  development  of  the  quantita- 
tive method  in  education. 

*A  charge  of  five  cents  a  copy  is  made  for  these  publications. 


17 


Some  Books  on  Education  Published  by  the 
Russell  Sage  Foundation 
Medical  Inspection  of  Schools.     Luther  H.  Gulick,  M.D., 
and  Leonard   P.  Ayres,   Ph.D.     276  pp.     Price,   postpaid, 
$1.00.     Charities   PubHcation   Committee,    105   East  22nd 
Street,  New  York  City. 
Gives  in  convenient  form  information  about  the  historical, 
educational,  administrative,  and  legal  phases  of  the  work.     (Now 
in  process  of  revision.) 

Laggards  in  our  Schools.     Leonard  P.  Ayres,  Ph.D.     236  pp. 
Price,  postpaid,  $1.50.     Charities  Publication  Committee, 
105  East  22nd  Street,  New  York  City. 
A  study  of  the  over-age  child,  the  child  who  repeats  grades, 
and  the  falling  out  of  school  of  pupils  before  the  completion  of 
the  course  in  American  city  school  systems.     It  is  illustrated  with 
some  forty  charts  and  diagrams,  and  its  inter-city  comparisons 
are  set  forth  in  nearly  one  hundred  tables.     Third  edition. 
Wider  Use  of  the  School  Plant.     Clarence  Arthur  Perry.     In- 
troduction by  Luther  H.   Gulick,   M.D.     423  pp.     Price, 
postpaid,    $1.25.     Charities    Publication    Committee,    105 
East  22nd  Street,  New  York  City. 
All  the  activities,  from  evening  schools  to  social  centers,  now 
carried  on  after  school  hours  in  school  buildings  are  described 
in  this  book.     It  shows  them  in  actual  operation,  outlines  the 
various  forms  of  administration  and  gives  pertinent  details  as 
to  cost,  development,  and  the  social  amelioration  which  they  are 
effecting.     Fully    illustrated    and    helpfully    indexed.     Second 
edition. 

Seven  Great  Foundations.     Leonard    P.   Ayres,    Ph.D.     79 
pp.     Price,    postpaid,    35    cents.     Department    of    Child 
Hygiene,  Russell  Sage  Foundation,  400  Metropolitan  Tower, 
New  York  City. 
Information  concerning  the  origin,  purposes,  activities  and 
history  of  the  following  foundations:   Peabody  Education  Fund, 
John  F.  Slater  Fund  for  the  Education  of  Freedman,  Carnegie 
Institution  of  Washington,  The  General  Education  Board,  Car- 
negie  Foundation  for  the  Advancement  of  Teaching,   Russell 
Sage  Foundation,  and  the  Anna  T.  Jeanes  Foundation. 
Open  Air  Schools.  Leonard  P.  Ayres,  Ph.D.  171pp.  Price$i.20 
(postage   12  cents).     Doubleday,  Page  &  Co.,  New  York. 
This  volume  gives  the  important  and  significant  American 
and  foreign  material  with  respect  to  outdoor  schools.     It  de- 
scribes the  English,  German  and  American  types,  gives  the^  re- 
sults and  furnishes  definite  information  with  respect  to  clothing, 
food,  cost,  administration,  etc.      It  has  more  than  70  pages  of 
illustrations  and  diagrams.     Bibliography. 

18 


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To  il  sasure  the  quality  of  a  sample  of  handwriting  slide  it  along  the  scale  until 
a  wJ  ;ing  of  corresponding  quality  is  found.  The  nunrvbdr  in  black  at  the  top 
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Printed       February 
R«prlnte4  M*rch. 
Reprinted  Mky. 


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